A combinatorial auction is an auction where the bidders have the choice to bid on bundles of items. The WDP in combinatorial auctions is the problem of finding winning bids that maximize the auctioneer’s revenue under the constraint that each item can be allocated to at most one bidder. The WDP is known as an NP-hard problem with practical applications like electronic commerce, production manag...

In this paper, we shall give an average case analysis of a mechanical theorem proving algorithin based upon branching techniques for solving the k--satisfiability problem. The branching algorithm is a modified version of Monien and Speckenmeyer's branching algorithm [Monien and Speckenmeyer 1985]. Monien and Speckenmeyer's branching algorithm has a worst case time complexity which is strictly b...

We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is...

Let X be either the branching diffusion corresponding to the operator Lu + β(u2 − u) on D ⊆ Rd [where β(x) ≥ 0 and β ≡ 0 is bounded from above] or the superprocess corresponding to the operator Lu + βu − αu2 on D ⊆ Rd (with α > 0 and β is bounded from above but no restriction on its sign). Let λc denote the generalized principal eigenvalue for the operator L + β on D. We prove the following dic...

We report on a symbolic approach to solving constraint problems, which uses relation algebra. The method gives good results for problems with constraints that are relations on intervals. Problems of up to 500 variables may be solved in expected cubic time. Strong evidence is presented that signi cant backtracking on random problems occurs only in the range 6 n:c 15, for c 0:5, where n is the nu...

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear P...